Vertex-Transitive Graphs which are not Cayley Graphs, I

Abstract

The Petersen Graph on 10 vertices is the smallest example of a vertex-transitive Graph which is. not a Cayley graph. We consider the problem of determining the orders of such graphs. in This, The first of a series of papers, we present a sequence of constructions which solve the problem for many orders. in particular, such graphs exist for all orders divisible by a fourth power, and all even orders which are divisible by a square. © 1994, Australian Mathematical Society. All rights reserved.